Problem: Example

Input

8 5
1 2
6 5
6 4
1 3
4 7


Output

11

Solution (in CPP):

Solution:
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<complex>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
using namespace std;
typedef long long ll;
typedef unsigned long long ul;
typedef unsigned int ui;
const ll mod = 1000000007;
typedef double ld;
typedef complex<ld> Point;
const ll INF = mod * mod;
typedef pair<int, int> P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
const ld eps = 1e-8;
const ld pi = acos(-1.0);
typedef pair<ld, ld> LDP;
typedef pair<ll, ll> LP;

vector<int> G[1 << 17];
bool used[1 << 17];
int col[1 << 17];

bitset<100001> b;

void solve() {
	int n, m; cin >> n >> m;
	rep(i, m) {
		int a, b; cin >> a >> b; a--; b--;
		G[a].push_back(b);
		G[b].push_back(a);
	}
	vector<P> v;
	rep(i, n) {
		if (used[i])continue;
		int c[2] = {};
		int id = 0; queue<int> q;
		q.push(i); used[i] = true; col[i] = 0;
		while (!q.empty()) {
			id ^= 1;
			int len = q.size();
			c[id^1] += len;
			rep(aa, len) {
				int v = q.front(); q.pop();
				rep(j, G[v].size()) {
					int to = G[v][j];
					if (used[to]) {
						if (col[to] == col[v]) {
							cout << -1 << endl; return;
						}
						continue;
					}
					used[to] = true; col[to] = id;
					q.push(to);
				}
			}
		}
		v.push_back({ c[0],c[1] });
	}
	b[0] = 1;
	rep(i, v.size()) {
		b = (b << v[i].first) | (b << v[i].second);
	}
	ll ans = 0;
	rep(i, n + 1) {
		if (b[i]) {
			//cout << i << endl;
			ans = max(ans,(ll)i*(n - i) - m);
		}
	}
	cout << ans << endl;
}
int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	solve();
	//stop
	return 0;
}